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d) Prove: If z = zo is a zero of order n of flz), then it is zero. of order 2n of (f(z))²

d) Prove: If z = zo is a zero of order n of flz), then it is zero. of order 2n of (f(z))²

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Questions: 1 part b question 3 1 part d
1) a) Find the zeros and their order for the following functions. 1) Z³ cos z 2) COS(23) 3) Coszt sinh (2) b) Find the order of Z=0 for the following functions: 25 1) 142-e2 2) 6 sin(z)+29-623 3) (ez²-1-2²) Sin³z c) If zo is a zero of order n of an analytic function f(z) and it is zero of order me of an analytic function g(z), what can be said about zo for the following functions: 1) f(z)+g(z) 2) (2)કુ(૨) 112) 3) giz) d) Prove: If z = zo is a zero of order n of f(z), then it is zero of order 2n of (f(z))2
Transcribed Image Text:1) a) Find the zeros and their order for the following functions. 1) Z³ cos z 2) COS(23) 3) Coszt sinh (2) b) Find the order of Z=0 for the following functions: 25 1) 142-e2 2) 6 sin(z)+29-623 3) (ez²-1-2²) Sin³z c) If zo is a zero of order n of an analytic function f(z) and it is zero of order me of an analytic function g(z), what can be said about zo for the following functions: 1) f(z)+g(z) 2) (2)કુ(૨) 112) 3) giz) d) Prove: If z = zo is a zero of order n of f(z), then it is zero of order 2n of (f(z))2
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